[Paper Review] Distributional data analysis with accelerometer data in a NHANES database with nonparametric survey regression models

Marcos Matabuena, Alex Petersen|arXiv (Cornell University)|Apr 2, 2021

Physical Activity and Health66 references4 citations

TL;DR

This paper introduces a novel distributional representation of accelerometer data to preserve rich, high-resolution physical activity patterns while accounting for complex survey designs in NHANES (2003–2006). By extending nonparametric functional models—kernel smoother and kernel ridge regression—to incorporate survey weighting and design effects, it enables reliable prediction of health outcomes in individuals over 68 years old, overcoming limitations of traditional summary metrics that discard detailed activity data.

ABSTRACT

Accelerometers enable an objective measurement of physical activity levels among groups of individuals in free-living environments, providing high-resolution detail about physical activity changes at different time scales. Current approaches used in the literature for analyzing such data typically employ summary measures such as total inactivity time or compositional metrics. However, at the conceptual level, these methods have the potential disadvantage of discarding important information from recorded data when calculating these summaries and metrics since these typically depend on cut-offs related to intensity exercise zones that are chosen subjectively or even arbitrarily. Much of the data collected in these studies follow complex survey designs, making application of standard statistical tools such as non-parametric regression models inappropriate and the requirement of specific estimation procedures according to particular sampling-design is mandatory. With functional data or other complex objects, barely literature exist that handles complex sampling designs in the statistical analysis. This paper aims two-fold; first, we introduce a new functional representation of accelerometer data of a distributional nature to build a complete individualized profile of each subject's physical activity levels. Second, using the NHANES accelerometer data (2003-2006), we show the potential advantages of this new representation to predict patients' outcomes over $68$ years of age. A critical component in our statistical modeling is that we extend non-parametric functional models used: kernel smoother and kernel ridge regression, to handle the specific effect of complex sampling design in order to provide reliable conclusions about the influence of physical activity in distinct analysis performed.

Motivation & Objective

• To address the loss of detailed physical activity information caused by conventional summary metrics based on arbitrary intensity cut-offs.
• To develop a functional, distributional representation of accelerometer data that captures individualized activity profiles across time scales.
• To extend nonparametric functional regression models—kernel smoother and kernel ridge regression—for complex survey designs to ensure valid inference.
• To evaluate the predictive performance of this new method in estimating health outcomes among individuals over 68 years of age in NHANES.

Proposed method

• Propose a distributional representation of accelerometer data that models the full distribution of activity counts over time, rather than relying on summary statistics.
• Apply nonparametric kernel smoothing and kernel ridge regression to model the relationship between the full activity distribution and health outcomes.
• Incorporate survey design features—such as stratification, clustering, and sampling weights—into the kernel estimation process to ensure design-based inference.
• Use weighted local estimating equations to adjust for unequal selection probabilities and survey design effects in functional regression.
• Implement design-consistent bandwidth selection and variance estimation to maintain statistical validity under complex sampling.
• Validate the method using NHANES accelerometer data (2003–2006) with outcomes defined for participants over 68 years old.

Experimental results

Research questions

• RQ1 Can a distributional representation of accelerometer data better preserve the richness of physical activity patterns compared to traditional summary metrics?
• RQ2 How can nonparametric functional regression models be adapted to handle complex survey designs in functional data analysis?
• RQ3 Does the proposed method improve the prediction of health outcomes in older adults compared to standard approaches?
• RQ4 What is the impact of survey design adjustments on the estimation accuracy and inference in functional regression models applied to accelerometer data?

Key findings

• The proposed distributional representation successfully captures individualized physical activity patterns across multiple time scales, retaining information lost in conventional summary metrics.
• The extension of kernel smoother and kernel ridge regression to complex survey designs enables valid statistical inference while preserving functional data structure.
• The method demonstrates improved predictive performance for health outcomes in individuals over 68 years old compared to models using summary statistics.
• Survey design adjustments significantly affect variance estimation and confidence intervals, highlighting the necessity of incorporating sampling weights in functional models.
• The approach reduces bias in effect estimation by accounting for unequal selection probabilities and clustering in the NHANES data.